Sectionally Pseudocomplemented Posets

Abstract The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension relative pseudocomplementation for not necessarily distributive lattices. typical example such is the non-modular N 5 . aim this paper to extend sectional from lattices posets. At first we show that class forms variety which can be described by two simple identities. This has nice congruence properties. We summarize properties posets and differences pseudocomplementation. prove every poset completely L -semidistributive. introduce on these when quotient structure becomes again. Finally, study Dedekind-MacNeille completion contrary case relatively posets, need but present construction so-called generalized ordinal sum enables us construct provided completions summands are known.